CN106863014A - A kind of five-axle number control machine tool linear axis geometric error detection method - Google Patents

Abstract

A kind of five-axle number control machine tool linear axis geometric error detection method of the present invention belongs to machine tool accuracy detection technique field, is related to a kind of linear axis error-detecting of five-axle number control machine tool and discrimination method.In detection method, three mesh measurement apparatus are built using three high resolution cameras, the three self-luminous feature target ball images for moving along a straight line are done in collection fixation with lathe X-axis or Y-axis on the table；By camera calibration, characteristic point position information extraction and three fusions of camera measurement information, the centre of sphere three-dimensional coordinate of feature target ball, measurement lathe X, the linear axis geometric error of Y-axis are obtained.The method effectively raises Digit Control Machine Tool linear axis error measure efficiency, avoid the identification model and cumbersome measurement process of complexity, realize the measurement of Digit Control Machine Tool linear axis geometric error, with convenient, fast, anti-noise ability it is strong, robustness is good, can simultaneously measure multinomial lathe linear axis geometric error the characteristics of.

Description

A kind of five-axle number control machine tool linear axis geometric error detection method

Technical field

The invention belongs to machine tool accuracy detection technique field, be related to a kind of linear axis error-detecting of five-axle number control machine tool with Discrimination method.

Background technology

With Aeronautics and Astronautics, the development of marine technology, all classes are increasingly becoming across the part of mesostructure with complex space The core component in field.Additionally, these parts such as engine impeller, marine propeller etc. are that the enough intensity of guarantee and rigidity are normal Frequently with complicated technology, efficient, the high-quality processing of part directly affects the standby service behaviour of dressing, there is very high wanting to machine tool capability Ask.Five-axle number control machine tool is widely used in complicated difficult processing part manufacture by high flexibility and high accuracy processed edge. However, Machine Tool design and the accuracy of manufacture limit the machining accuracy of five-axle number control machine tool.Geometric precision of machine tool directly affect by The machining accuracy of part is processed, to improve part processing precision, the accurate detection of lathe items geometric error is significant. Lathe linear axis geometric error is the important component of lathe geometric error, periodic detection lathe linear axis geometric error so as to It is significant for improving Digit Control Machine Tool machining accuracy for error compensation provides data supporting.

The detection means of current five-axle number control machine tool linear axis geometric error mainly has：Grating examinations method, laser interferometer Method and level measurement method etc..The A of Patent No. CN 104097114 of Shenyang lathe Co., Ltd Liu Kuo inventions are " a kind of The geometric error measurement of multi-shaft linkage numerical control machine and isolation technics " has invented a kind of axle lathe of use laser interferometer measurement three 15 methods of error, but use the laser interferometer measurement cycle it is long, error can only individual event detection, it is impossible to realize multinomial error Synchronous detection；A kind of A of Patent No. CN 103737426 " Digit Control Machine Tool rotary shafts of Xi'an Communications University's Guo Junjie invention The line mensuration of geometric error three " realizes the measurement of rotary axis of machine tool geometric error using laser tracker and supporting opal, Certainty of measurement is limited to laser tracker corner positioning precision, and measuring apparatus are relatively costly.

The content of the invention

The invention solves the problems that technical barrier be to overcome existing technological deficiency, invent a kind of five-axle number control machine tool linear axis Geometric error detection method, using the feature target ball being fixed on during three cameras collection machine tool motions on platen Positional information, the measurement of the multinomial geometric error of lathe linear axis is completed by image, data processing.Any two between three cameras The optical axis of individual camera is mutually perpendicular to, and three optical axises of camera are parallel with three reference axis difference of lathe coordinate system.Numerical control system System control platen moves along a straight line along lathe X-axis and Y-axis respectively, using feature target ball position in camera collection motion process Put image.By image procossing, reconstruction obtains the feature target ball centre of sphere three-dimensional coordinate for characterizing machine tool motion position, and and machine Bed theory movement position forms plane compared to straightness error, position error and the lathe X-axis and Y-axis for obtaining lathe linear axis Flatness error.The method uses self-luminous feature target ball, and not only image characteristics extraction high precision, and program is simple, surveys Amount method has robustness very high, and measuring speed is fast, can simultaneously measure multinomial error.

The technical solution adopted by the present invention is a kind of five-axle number control machine tool linear axis geometric error detection method, its feature It is in detection method, three mesh measurement apparatus to be built using three high resolution cameras, collection is fixed on platen random Bed X-axis or Y-axis do self-luminous A, B, C the feature target ball image for moving along a straight line；By camera calibration, characteristic point position information extraction With three fusions of camera measurement information, the centre of sphere three-dimensional coordinate of feature target ball, measurement lathe X, the linear axis geometry of Y-axis are obtained Error；Detection method is comprised the following steps that：

The first step builds three mesh measurement apparatus, and carries out camera calibration；

When building, any two camera optical axis are mutually perpendicular in three cameras, constitute space measurement coordinate system；No. 1 camera 1 , parallel to lathe X-direction, parallel to lathe Y direction, No. 3 optical axises of camera 3 are parallel to lathe master for No. 2 optical axises of camera 2 for optical axis Axle Z-direction, it is ensured that the coordinate system being made up of camera optical axis is identical with lathe coordinate system direction, by No. 1, No. 2, No. 3 cameras 1,2,3 It is separately fixed in camera adjustment frame 4；

Camera calibration is carried out, camera calibration is to camera intrinsic parameter (α_x,α_y,u₀,v₀) and outer parameter [R T] solution；Three The one-to-one relationship that individual camera is set up between image coordinate system and world coordinate system by pin-hole imaging model；It is three-dimensional using 3D Target standardization is demarcated respectively to three cameras；It demarcates expression formula：

Wherein,M represents projection matrix, m_ijRepresent the i rows j row unit of projection matrix Element；(X_wi,Y_wi,Z_wi, 1) and represent the i-th point of coordinate in world coordinate system, (u in 3D stereo targets_i,v_i, 1) represent i-th The image coordinate of point, s represents scale factorThe intrinsic parameter of camera is represented, [R T] represents the outer ginseng of camera Number；

The installation of second step feature target ball and feature target ball image procossing

Three A, B, C feature target balls 6,5,7 are respectively mounted on platen 8, A features target ball 6 is first arranged on machine Bed table core, B, C feature target ball 5,7 is separately mounted to the both sides of A features target ball 6, and regulation feature target ball works in lathe Position on platform 8, makes it be imaged in three viewing field of camera and does not block mutually completely；Three feature target balls have different diameters, That is d_A＞ d_B＞ d_C, feature target ball diameter difference is easy to the matching of image feature information in different cameral；

Be it is accurate extract feature target ball sphere centre coordinate, image by noise reduction, after filtering process, using the gray scale with threshold value Gravity model appoach extracts the centre of sphere of feature target ball, and computing formula is：

WhereinF (x, y) represents gradation of image function, and f (x, y) represents image Gray scale, T represents background threshold；(x₀,y₀) required grey scale centre of gravity, m are represented, n represents what image was included on horizontal, longitudinal direction The quantity of pixel；The image coordinate of the feature target ball centre of sphere can be extracted using the gray scale center method with threshold value；

3rd pacing amount lathe X, the linear axis geometric error of Y-axis,

Lathe X, the linear axis geometric error of Y-axis include position error, straightness error, lathe flatness error；With machine As a example by the geometric error of bed X-axis is solved, it is described in detail, the linear axis geometric error solution of Y-axis is identical with X-axis；

Constitute measurement coordinate system by camera optical axis, and overlapped with world coordinate system foundation at lathe zero point, digital control system Control machine bed is moved in the X-axis direction；Selected measurement range is N (mm) × N (mm), effective range is divided into L sections, relatively L+1 data acquiring location should be obtained, the positional information of acquisition characteristics target ball at this L+1 data acquiring location；Through image Feature information extraction, solves feature target ball centre of sphere three-dimensional coordinate in measurement coordinate system, is used to characterize the actual motion letter of lathe Breath；

When the position error of lathe X-direction is measured, platen 8 is moved along lathe X-direction, in measurement process In, in the camera due to feature target ball in No. 1 optical axis of camera 1 parallel to lathe X-direction, there is the change in depth of field direction in its imaging Change, therefore super depth of field phenomena impair measurement result occurs；And the imaging of feature target ball does not exist in No. 2 cameras 2 and No. 3 cameras 3 Depth of field direction change, therefore solve the data gathered using No. 2 cameras 2 and No. 3 cameras 3 during lathe X-axis position error；Lathe worker Make platform 8 to move at lathe zero point, lathe zero point is also simultaneously the zero point of measurement coordinate system and world coordinate system, will now each phase Image based on the image of machine collection, No. 2 cameras 2 survey be k-th o'clock relative to first point in measurement coordinate system X-direction Variable quantity dx and the change dz in measurement coordinate system Z-direction, No. 3 measurements of camera 3 are k-ths o'clock relative to first point Variable quantity dx in the measurement coordinate system X-direction and change dy in measurement coordinate system Y-direction, by measuring letter in two cameras The fusion of breath, obtains three-dimensional coordinate of the K points in measurement coordinate system, is denoted asWherein i represents the survey at K points Amount number of times, i=1,2 ... n；

4th step lathe linear axis Error Analysis are solved

A) position error is solved

The positioning precision of lathe linear axis refers to that lathe is positioned to the levels of precision of program object point；Position error is lathe Actual location point deviates the numerical value of program object point；

Position error solution formula：

Wherein,The actual coordinate that expression is obtained in k-th measurement point i ＆ lt measurement,Represent and surveyed at k-th point The average localization error that amount is i times, δ_kRepresent the standard deviation of k-th measurement point position error, δ_xRepresent the positioning of lathe X-axis Error；

B) straightness error is solved

Measurement lathe X-axis straightness error is the same with position error, is using No. 2 cameras 2 and No. 3 acquisition characteristics of camera 3 Target ball movable information；Feature target ball sphere center position is solved, is compared with ideal position and is obtained straightness error；K measurement points are being surveyed Amount coordinate system in coordinate beI represents that k-th measurement point i ＆ lt is measured, and is commented using least square method Determine lathe linear axis straightness error；

Multiple measurement results to k-th measurement point are processed, that is, seek the average value of multiple measurement：It is designated asThe actual coordinate of k-th measurement point is represented, wherein,

Using least square fitting space line equation：

Ax+By+Cz+D=0 (5)

Wherein, A, B, C, D are space line equation coefficient

Wherein,Represent and the multiple measurement results of k-th point are averaging, and now K points are represented with it Actual position information；Represent respectively measurement point Y-coordinate apart from fitting a straight line maximum Y-direction distance and minimum Y-direction away from From；Represent measurement point Z coordinate apart from the maximum Z-direction distance of fitting a straight line and minimum Z-direction distance, A, B, C, D respectively It is space line equation coefficient；

Wherein,The straightness error in lathe X-axis Y-direction is represented,Represent the straight line in lathe lathe X-axis Z-direction Degree error；

C) lathe flatness error measurement

By No. 2 cameras 2 and the geometric error of No. 3 measurement in a closed series lathe X-directions of camera 3, No. 1 camera 1 and No. 3 cameras 3 The geometric error of measurement in a closed series lathe Y direction, the three-dimensional coordinate of lathe X-direction measurement point and lathe Y direction are measured The three-dimensional coordinate synthesis of point, is denoted as a cloud space U, and it is three-dimensional that U represents lathe linear axis actual motion position in effective range Coordinate information；Go out the plane motion equation of machine tool motion in effective range using least square method Optimal Fitting, with reference to flat The least square method of face degree error judges method, can measure the lathe plane motion caused by lathe linear axis geometric error and miss Difference；The point in a cloud U, P=(X are represented with P_p,Y_p,Z_p),P∈U；Evaluation lathe flatness error is set up using least square method Fitting datum plane；

Z=aX+bY+c (9)

Wherein, a, b, c are plane equation coefficient

In formula, (X_p,Y_p,Z_p) it is point in a cloud U, h_maxRepresent measurement point Z coordinate to the maximum Z-direction of fitting datum plane Distance, h_minMeasurement point Z coordinate to the minimum Z-direction distance of fitting datum plane is represented, using ultimate range and the difference of minimum range Value characterizes lathe flatness error；Flatness error：

η=h_max-h_min (11)

The measurement analysis and solution of Digit Control Machine Tool linear axis geometric error is more than completed, including position error, linearity are missed Difference and flatness error.

The beneficial effects of the invention are as follows three mesh camera combination self-luminous feature target balls are utilized, realize that Digit Control Machine Tool linear axis are several The measurement of what error, including straightness error, flatness error and position error.With convenient, fast, anti-noise ability is strong, Shandong Rod is good, and the advantage of the multinomial error of lathe linear axis can be simultaneously measured in the case where not needing other axles to coordinate.The method is effectively carried High Digit Control Machine Tool linear axis error measure efficiency, it is to avoid complicated identification model and cumbersome measurement process, are numerical control machine The bed method that has provided of other error-detectings.

Brief description of the drawings

Fig. 1 is lathe linear axis geometric error detection means figure, wherein, 1-1 cameras, 2-2 cameras, 3-3 cameras, 4- camera adjustment frames, 5-B feature target balls, 6-A feature target balls, 7-C feature target balls, 8- platens.

Fig. 2 is lathe linear axis error measure flow chart.

Specific embodiment

Specific embodiment of the invention is described in detail below in conjunction with technical scheme and accompanying drawing.

The present invention uses 3 cameras, and collection fixation follows lathe to do the feature target ball image for moving along a straight line on the table Information, is processed through aggregation of data, solves lathe linear axis geometric error.Fig. 1 is the lathe linear axis geometry based on trinocular vision Error detecting apparatus figure, No. 1, No. 2, No. 3 cameras 1,2,3 are separately mounted in camera adjustment frame 4, then by B, A, C feature target Ball 5,6,7 is separately mounted on platen 8.

Adjusting the position of each camera makes No. 1 optical axis of camera 1 parallel to lathe X-direction；No. 2 optical axises of camera 2 are parallel to machine Bed Y direction；No. 3 optical axises of camera 3 are perpendicular to platen plane.The present invention uses 3 same model high resolution cameras, phase Machine resolution ratio is：4096 × 3072, frame frequency：180fps, matches camera lens：Nikon24/70 ordinary zoom lens, lens focus： 24-70mm, Lens：83mm × 133mm (diameter × length), camera lens weight：900g, subject away from：460mm, camera lens is burnt Away from：40mm, measurement range is set to：150mm×150mm.

The specific detecting step of detection method is as shown in Figure 2：

(1) camera calibration

Target is demarcated using 3D to demarcate three cameras respectively, image coordinate system and generation are set up by pin-hole imaging model Relation between boundary's coordinate system.Three cameras are demarcated respectively, and camera model calibrating parameters are solved using formula (1).Every camera Calibrating parameters combining camera position distribution situation in space, merge out the three of the feature target ball centre of sphere using each camera information Dimension information.

(2) feature target ball is installed

The present invention characterizes lathe linear axis movable information using the feature target ball for fixedly mounting on the table.The present invention The self-luminous feature target ball size for being used is different, and a diameter of 20mm of A features target ball 6, B features target ball 5 a diameter of 15mm, C are special Levy the diameter 10mm of target ball 7.In order that feature target ball has the picture of complete display in each camera, it is ginseng with A features target ball 6 Sighting target is accurate, A features target ball 6 first is arranged on into table core, then install B features target ball 5 and C features target ball 7, B features target ball 5 It is (20,20) relative to the coordinate of A features target ball 6, C features target ball 7 is (- 15, -15) relative to the coordinate of A features target ball 6, Ensure that 3 feature target balls do not block the picture of complete display mutually.

(3) image characteristics extraction

Three cameras are in the positional information of different angles acquisition characteristics target ball simultaneously, and feature target ball is magazine at three Imaging is all circle.It is accurately to extract feature target ball sphere center position information because image background information is complex, in image filter After ripple, de-noising, using the grey scale centre of gravity method for adding threshold value, effectively distinguish background, accurately extract the centre of sphere.Specific threshold value T is according to image Background it is different and different, background is more complicated, and threshold value T values are bigger, and initial threshold takes 6000.It is special feature to be calculated using formula (2) Levy target ball sphere centre coordinate information.

(4) lathe linear axis geometric error measurement

It is 150mm × 150mm that measurement range is selected in the present invention, is now specifically measured with lathe X-direction geometric error As a example by journey, the effective range of lathe X-direction is 150mm, is divided into 50 sections, i.e., carrying out a secondary data per 3mm adopts Collection, the effective range of lathe Y direction is 150mm, is divided into 10 sections.Setting lathe is along X-direction feed speed It is 1m/min, lathe reset is on measurement range edge line, it is stipulated that first along lathe X-axis positive movement to measure positive direction First digital control system control workbench is moved along lathe X-axis negative direction, and initial position is designated as measuring near point, and is gathered with three mesh cameras Data, to measurement final position, are designated as measuring far point, when, control workbench continues to move 10mm to lathe X-axis negative direction, so Counter motion 10mm, eliminates the influence that hysterisis error is caused afterwards.Digital control system control workbench along lathe X-axis positive movement until Measurement near point, equally carries out eliminating the operation of hysterisis error at measurement near point, repeats the process 5 times, and control workbench is along machine Bed Y direction movement 10mm, repeats above-mentioned measurement process, and total obtains 75 groups of measurement data.

(5) lathe linear axis Error Analysis are solved

Camera understands by the corresponding physical size of pixel in every camera image after demarcation, p₁In expression camera 1 The corresponding physical size of one pixel, p₂Represent the corresponding physical size of pixel, p in camera 2₃Represent a picture in camera 3 The corresponding physical size of element.The origin of the measurement coordinate system of the present embodiment is first measurement point, identical with lathe zero point.Three mesh Vision measurement is follow-up measurement point relative to first position deviation of point, in the error of measurement lathe X-direction linear axis When, follow-up measurement point is measured relative to starting point in measurement coordinate system X-direction using 3, No. 2 cameras 2 of No. 2 cameras 2 and No. 3 cameras With the variation of Z-direction, Δ x is denoted as respectively₁With Δ z, No. 3 cameras 3 measure follow-up measurement point relative to starting point in measurement coordinate It is the variation of X-direction and Y-direction, Δ x is denoted as respectively₃With Δ y, due to there is two variable quantities of X-direction, in computation and measurement point X During the coordinate in direction, use the average value of physical size forEach picture is multiplied by using respective image size The physical size that element is represented can converse specific coordinate value, be denoted asI represented in k-th measurement point, Coordinate information during i measurement, the present invention is in each measurement point repeated acquisition data 10 times, therefore i ∈ 1,2...10.

The present invention is judged lathe position error using iso standard, each measurement point gathered data 10 times.To every 10 secondary datas at individual point are processed respectively：Obtain the standard deviation δ of each measurement point position error_k.Solve each measurement The 3 δ decision-points at point place, by the sequence of all decision-points, with the difference sign lathe of maxima and minima in decision-point a little Position error is specific to solve using formula (3) and formula (4).

Linearity geometric error：The actual straight line of limitation refers to tested straight line to a kind of form tolerance of ideal line variation Relative to the minimum change amount of ideal line.Lathe straight line error is judged using least square method rating method, by measuring Data pointGo out to judge datum line using least square fitting, Y-coordinate is arrived in solving measurement point using formula (6) The maximum Y-direction distance of datum lineWith minimum Y-direction distanceLathe Y is characterized using the difference of ultimate range and minimum range To straightness errorMeasurement point Z coordinate to the maximum Z-direction distance of datum line is solved using formula (7)With minimum Z-direction away from FromLathe Z-direction straightness error is characterized using the difference of ultimate range and minimum range

Flatness geometric error：Minimum change amount of the tested physical plane relative to ideal plane.The present invention is using minimum Square law rating method is judged lathe flatness error, and the data point obtained using measurement is fitted the benchmark of bed plane motion Equation, concrete form shows as formula (9), solves the maximum Z-direction variation h of Z coordinate relative datum equation in measurement point_maxWith Minimum Z-direction variation h_min, shown in solution procedure such as formula (10).With maximum Z-direction variation h_maxWith minimum Z-direction variation h_min Difference characterize lathe flatness error.

The method effectively raises Digit Control Machine Tool linear axis error measure efficiency, it is to avoid complicated identification model and numerous Trivial measurement process, realizes the measurement of Digit Control Machine Tool linear axis geometric error, with convenient, fast, anti-noise ability is strong, robustness Well, the characteristics of can simultaneously measuring multinomial lathe linear axis geometric error.

Claims (1)

1. a kind of five-axle number control machine tool linear axis geometric error detection method, it is characterized in that, in detection method, using three high scores Resolution camera builds three mesh measurement apparatus, and collection is fixed on platen and move along a straight line spontaneous is done with lathe X-axis or Y-axis Light A, B, C feature target ball image；By camera calibration, characteristic point position information extraction and three fusions of camera measurement information, Obtain the centre of sphere three-dimensional coordinate of feature target ball, measurement lathe X, the linear axis geometric error of Y-axis；The specific steps of detection method are such as Under：

The first step builds three mesh measurement apparatus, and carries out camera calibration；

When building, any two camera optical axis are mutually perpendicular in three cameras, constitute space measurement coordinate system；No. 1 camera (1) light , parallel to lathe X-direction, parallel to lathe Y direction, No. 3 camera (3) optical axises are parallel to lathe for No. 2 camera (2) optical axises for axle Main shaft Z-direction, it is ensured that the coordinate system being made up of camera optical axis is identical with lathe coordinate system direction, by No. 1, No. 2, No. 3 cameras (1, 2nd, 3) it is separately fixed in camera adjustment frame (4)；

Camera calibration is carried out, camera calibration is to camera intrinsic parameter (α_x,α_y,u₀,v₀) and outer parameter [R T] solution；Three phases The one-to-one relationship that machine is set up between image coordinate system and world coordinate system by pin-hole imaging model；Using 3D stereo targets Standardization is demarcated respectively to three cameras；It demarcates expression formula：

$s\left[\begin{array}{c}{u}_i\\ v_i\\ 1\end{array}\right]=\left[\begin{array}{ccc}{\mathrm{\α}}_x& 0& u_0\\ 0& {\mathrm{\α}}_y& v_0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{cc}R& T\end{array}\right]\left[\begin{array}{c}{X}_{wi}\\ Y_{wi}\\ Z_{wi}\\ 1\end{array}\right]=M\left[\begin{array}{c}{X}_{wi}\\ Y_{wi}\\ Z_{wi}\\ 1\end{array}\right]---\left(1\right)$

Wherein,M represents projection matrix, m_ijRepresent the i row j column elements of projection matrix；(X_wi, Y_wi,Z_wi, 1) and represent the i-th point of coordinate in world coordinate system, (u in 3D stereo targets_i,v_i, 1) and represent i-th point of figure As coordinate, s represents scale factorThe intrinsic parameter of camera is represented, [R T] represents the outer parameter of camera；

The installation of second step feature target ball and feature target ball image procossing

Three A, B, C feature target balls (6,5,7) are respectively mounted on platen (8), first A features target ball (6) is arranged on Platen center, B, C feature target ball (5,7) is separately mounted to the both sides of A features target ball (6), and regulation feature target ball is in machine Position on bed workbench (8), makes it be imaged in three viewing field of camera and does not block mutually completely；Three feature target balls have difference Diameter, i.e. d_A>d_B>d_C, feature target ball diameter difference is easy to the matching of image feature information in different cameral；

Be it is accurate extract feature target ball sphere centre coordinate, image by noise reduction, after filtering process, using the grey scale centre of gravity with threshold value Method extracts the centre of sphere of feature target ball, and computing formula is：

$\begin{array}{cc}{x}_0=\frac{\underset{x=1}{\overset{m}{\mathrm{\Σ}}}\underset{y=1}{\overset{n}{\mathrm{\Σ}}}\[F\left(x,y\right)-T\]x}{\underset{x=1}{\overset{m}{\mathrm{\Σ}}}\underset{y=1}{\overset{n}{\mathrm{\Σ}}}F\left(x,y\right)}& y_0=\frac{\underset{x=1}{\overset{m}{\mathrm{\Σ}}}\underset{y=1}{\overset{n}{\mathrm{\Σ}}}\[F\left(x,y\right)-T\]y}{\underset{x=1}{\overset{m}{\mathrm{\Σ}}}\underset{y=1}{\overset{n}{\mathrm{\Σ}}}F\left(x,y\right)}\end{array}---\left(2\right)$

WhereinF (x, y) represents gradation of image function, and f (x, y) represents gradation of image, T represents background threshold；(x₀,y₀) required grey scale centre of gravity, m are represented, n represents the pixel that image is included on horizontal, longitudinal direction Quantity；The image coordinate of the feature target ball centre of sphere can be extracted using the gray scale center method with threshold value；

3rd pacing amount lathe X, the linear axis geometric error of Y-axis,

Lathe X, the linear axis geometric error of Y-axis include position error, straightness error, lathe flatness error；With lathe X-axis Geometric error solve as a example by, be described in detail, the linear axis geometric error of Y-axis solves identical with X-axis；

Measurement coordinate system is constituted by camera optical axis, and foundation is overlapped with world coordinate system at lathe zero point, digital control system is controlled Lathe is moved in the X-axis direction；Selected measurement range is N (mm) × N (mm), and effective range is divided into L section, it is corresponding must To L+1 data acquiring location, the positional information of acquisition characteristics target ball at this L+1 data acquiring location；Through characteristics of image Information extraction, solves feature target ball centre of sphere three-dimensional coordinate in measurement coordinate system, is used to characterize the actual motion information of lathe；

When the position error of lathe X-direction is measured, platen (8) is moved along lathe X-direction, in measurement process In, in the camera due to feature target ball in No. 1 camera (1) optical axis parallel to lathe X-direction, there is depth of field direction in its imaging Change, therefore super depth of field phenomena impair measurement result occurs；And No. 2 cameras (2) and No. 3 interior feature target ball imagings of camera (3) In the absence of depth of field direction change, therefore gathered using No. 2 cameras (2) and No. 3 cameras (3) when solving lathe X-axis position error Data；Platen (8) is moved at lathe zero point, and lathe zero point is also simultaneously the zero of measurement coordinate system and world coordinate system Point, by image based on the now image of each camera collection, it is that k-th o'clock exists relative to first point that No. 2 cameras (2) are surveyed The variable quantity dx of the measurement coordinate system X-direction and change dz in measurement coordinate system Z-direction, No. 3 camera (3) measurements are K Individual o'clock relative to first point the variable quantity dx in measurement coordinate system X-direction and the change dy in measurement coordinate system Y-direction, warp The fusion of metrical information in two cameras is crossed, three-dimensional coordinate of the K points in measurement coordinate system is obtained, is denoted asIts Middle i represents the pendulous frequency at K points, i=1,2 ... n；

4th step lathe linear axis Error Analysis are solved

A) position error is solved

The positioning precision of lathe linear axis refers to that lathe is positioned to the levels of precision of program object point；Position error is lathe reality Anchor point deviates the numerical value of program object point；

Position error solution formula：

$\left\{\begin{array}{c}{X}_s^k=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{X}_i^k-{\mathrm{nX}}^k}{n}\\ {\mathrm{\δ}}_k=\frac{{\[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(X_i^k-X_s^k\right)}^2\]}^{\frac{1}{2}}}{n-1}\end{array}\right.---\left(3\right)$

${\mathrm{\δ}}_x=\left|max(X_s^k+3{\mathrm{\δ}}_k)\right|+\left|min(X_s^k-3{\mathrm{\δ}}_k)\right|,k\∈(1,L+1)---\left(4\right)$

Wherein,The actual coordinate that expression is obtained in k-th measurement point i ＆ lt measurement,Represent and measured i times at k-th point Average localization error, δ_kRepresent the standard deviation of k-th measurement point position error, δ_xRepresent the position error of lathe X-axis；

B) straightness error is solved

Measurement lathe X-axis straightness error is the same with position error, is using No. 2 cameras (2) and No. 3 camera (3) acquisition characteristics Target ball movable information；Feature target ball sphere center position is solved, is compared with ideal position and is obtained straightness error；K measurement points are being surveyed Amount coordinate system in coordinate beI represents that k-th measurement point i ＆ lt is measured, and is evaluated using least square method Lathe linear axis straightness error；

Multiple measurement results to k-th measurement point are processed, that is, seek the average value of multiple measurement：It is designated asThe actual coordinate of k-th measurement point is represented, wherein,

$X_e^k=\frac{\underset{1}{\overset{i}{\Σ}}{X}_i^k}{i},Y_e^k=\frac{\underset{1}{\overset{i}{\Σ}}{Y}_i^k}{i},Z_e^k=\frac{\underset{1}{\overset{i}{\Σ}}{Z}_i^k}{i};$

Using least square fitting space line equation：

Ax+By+Cz+D=0 (5)

Wherein, A, B, C, D are space line equation coefficient

$\left\{\begin{array}{c}{g}_{max}^y=max(Y_e^k+\frac{A}{B}{X}_e^k+\frac{C}{B}{Z}_e^k+\frac{D}{B})\\ g_{min}^y=min(Y_e^k+\frac{A}{B}{X}_e^k+\frac{C}{B}{Z}_e^k+\frac{D}{B})\end{array}\right.---\left(6\right)$

$\left\{\begin{array}{c}{g}_{\max }^z=\max \left(Z_e^k+\frac{A}{C}{X}_e^k+\frac{B}{C}{Y}_e^k+\frac{D}{C}\right)\\ g_{\min }^z=\min \left(Z_e^k+\frac{A}{C}{X}_e^k+\frac{B}{C}{Y}_e^k+\frac{D}{C}\right)\end{array}\right.---\left(7\right)$

Wherein,Represent and the multiple measurement results of k-th point are averaging, and the actual bit of now K points is represented with it Confidence ceases；Represent measurement point Y-coordinate apart from the maximum Y-direction distance of fitting a straight line and minimum Y-direction distance respectively；Measurement point Z coordinate is represented respectively apart from the maximum Z-direction distance of fitting a straight line and minimum Z-direction distance, and A, B, C, D are sky Between linear equation coefficient；

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_x^y=g_{max}^y-g_{\min }^y\\ {\mathrm{\ϵ}}_x^z=g_{max}^z-g_{\min }^z\end{array}\right.---\left(8\right)$

Wherein,The straightness error in lathe X-axis Y-direction is represented,Represent that the linearity in lathe lathe X-axis Z-direction is missed Difference；

C) lathe flatness error measurement

By No. 2 cameras (2) and the geometric error of No. 3 camera (3) measurement in a closed series lathe X-directions, No. 1 camera (1) and No. 3 cameras (3) geometric error of measurement in a closed series lathe Y direction, the three-dimensional coordinate of lathe X-direction measurement point and lathe Y direction are surveyed The three-dimensional coordinate synthesis of point is measured, a cloud space U is denoted as, U represents lathe linear axis actual motion position three in effective range Dimension coordinate information；Go out the plane motion equation of machine tool motion in effective range using least square method Optimal Fitting, with reference to The least square method of flatness error judges method, the lathe plane motion error that measurement is caused by lathe linear axis geometric error； The point in a cloud U, P=(X are represented with P_p,Y_p,Z_p),P∈U；The plan of evaluation lathe flatness error is set up using least square method Close datum plane；

Z=aX+bY+c (9)

Wherein, a, b, c are plane equation coefficient

$\left\{\begin{array}{c}{h}_{\max }=\max \left(Z_p-{\mathrm{aX}}_p-{\mathrm{bY}}_p-c\right)\\ h_{\min }=\min \left(Z_p-{\mathrm{aX}}_p-{\mathrm{bY}}_p-c\right)\end{array}\right.---\left(10\right)$

In formula, (X_p,Y_p,Z_p) it is point in a cloud U, h_maxRepresent measurement point Z coordinate to be fitted datum plane maximum Z-direction away from From h_minMeasurement point Z coordinate to the minimum Z-direction distance of fitting datum plane is represented, using ultimate range and the difference of minimum range Characterize lathe flatness error；Flatness error：

η=h_max-h_min (11)

More than complete the measurement analysis and solution of Digit Control Machine Tool linear axis geometric error, including position error, straightness error and Flatness error.